Uniaxial cyclic visco-plastic behaviour of a nickel-based superalloy, RRIOOO, has been successfully described under strain-controlled conditions by Tong and associates using Chaboche type of models with two kinematic hardening components. In this work, the ability of the original model was evaluated to consider unbalanced stress-controlled conditions at selected stress ranges and ratios. A third kinematic hardening component was introduced in the constitutive model to enabled an improved solution with which both ratchetting and cyclic deformation can be modelled adequately. The role of each kinematic hardening parameter in the description of ratchetting was examined and discussed with respect to the modified model response.